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> stochastic simulation .. approximating the universe your education is showing.. perhaps you have a different definition of mathematics among many definition

> stochastic simulation .. approximating the universe your education is showing.. perhaps you have a different definition of mathematics among many definitions you can define mathematics as an abstract science or as what those abstractions are studying but holding the first definition is insufficient evidence for the inexistence of the second i'm unclear what you think intractable equations.. whether easy or difficult to form and what the definitions of easy and hard are or why they are of consequence.. say of mathematics a computer is a system literally built as an electrical manifestation of mathematics, albeit a subset, and in its case suffers limitations of intractability but the mathematics underlying its structure still remain can you defend the position that the limitations of a nand gate somehow disproves quantity(o)? also, I think Godel would be distressed to have heard the incompleteness theorems being used to deny the existence of mathematics incompleteness is intended to show mathematics exists beyond the scope of proof for me incompleteness does go beyond its intentions but as proof of paradox such as the existence mathematics (o) https://en.m.wikipedia.org/wiki/Quantity https://en.m.wikipedia.org/wiki/Quantity

CuriouslyC 10y ago
If you want to be so general, then anything can be considered mathematics, at which point it kind of loses its meaning. For me, mathematics is any system of symbolic manipulation built on top of axiomatic set theory, ideally having some algebraic structure. Given that the universe is comprised of things and not symbolic representations (unless you want to get really general about what a symbol is) that seems to disqualify it right there. Can we approximately describe the universe using mathematics? At the gross level, with the inclusion of fuzzy sets/probability theory, sure. At the fine level, I'm not so sure we can accurately represent the universe using less information than the universe itself contains - thus you aren't abstracting anything. I mentioned the incompleteness theorems because they suggest a universe that was a consistent logical system would be arbitrarily constrained from valid portions of its state space - a testable hypothesis with no evidence. Of course, if you toss out consistency then all bets are off.
- justifier 10y ago
  > If you want to be so general, then anything can be considered mathematics that was where this whole conversation started, 'what is reality[anything]?' you are working from an incomplete definition of the full scale of, even recognised, mathematics which is clear in that you define it as being 'built on top of axiomatic set theory' when godel used mathematics to show axioms are limited in scope but you, stead Godel, consider that all of mathematics, and now I'm repeating myself
- criddell 10y ago
  > Given that the universe is comprised of things and not symbolic representations In my original comment I was referring to the theory that the universe is entirely mathematics. I'm not talking about modeling with mathematics, rather that the universe is mathematics. There are no things.

CuriouslyC 10y ago

If you want to be so general, then anything can be considered mathematics, at which point it kind of loses its meaning. For me, mathematics is any system of symbolic manipulation built on top of axiomatic set theory, ideally having some algebraic structure. Given that the universe is comprised of things and not symbolic representations (unless you want to get really general about what a symbol is) that seems to disqualify it right there. Can we approximately describe the universe using mathematics? At the gross level, with the inclusion of fuzzy sets/probability theory, sure. At the fine level, I'm not so sure we can accurately represent the universe using less information than the universe itself contains - thus you aren't abstracting anything. I mentioned the incompleteness theorems because they suggest a universe that was a consistent logical system would be arbitrarily constrained from valid portions of its state space - a testable hypothesis with no evidence. Of course, if you toss out consistency then all bets are off.

justifier 10y ago
> If you want to be so general, then anything can be considered mathematics that was where this whole conversation started, 'what is reality[anything]?' you are working from an incomplete definition of the full scale of, even recognised, mathematics which is clear in that you define it as being 'built on top of axiomatic set theory' when godel used mathematics to show axioms are limited in scope but you, stead Godel, consider that all of mathematics, and now I'm repeating myself
criddell 10y ago
> Given that the universe is comprised of things and not symbolic representations In my original comment I was referring to the theory that the universe is entirely mathematics. I'm not talking about modeling with mathematics, rather that the universe is mathematics. There are no things.